First of all, please note, that interactions between regular and inverted objects are inconsistent in the film (archived):
tl;dr: Inverted things impact puddles and the impact propagates forward in time. Inverted things impact walls (and, apparently, people) and the impact propagates backwards in time. A non-inverted wall and a non-inverted puddle can not propagate impacts from inverted things in different time directions. That is an inconsistency.
To answer the actual question:
Is it possible that the car is actually inverted?
Yes, the car is inverted. Here's an explanation suggested by u/Krystman on subreddit r/tenet:
How can inverted Protagonist drive a non inverted car at normal speed since it would have to be in reverse gear, severely limiting its drive speed?
The car may be inverted as well. It reverse-flips onto the highway and reverse-explodes.
To add to this, here's timeline of the silver car (adapted from another reddit comment):
Timeline of the silver car:
Creation → Life as a regular car → Inversion → Parked outside at the docks (near exit out of Turnstile) → Crashed → Exploded
After the crash, inverted Sator lights it up with inverted cigarette lighter. But then it is shown that the explosion resulting from it is a regular explosion with regular entropy. The inverted car and inverted protagonist experience the increase in entropy caused by explosion in reverse—for them, it is a decrease in entropy, and thus they are freezing. The windows on the inverted car get covered in ice and the inverted protagonist gets hypothermia.
It was very hard to catch in the film, but Neil explains that when two types of entropy (regular and inverted) interact, the regular wins: "It's like pissing in the wind". So regular entropy of oxygen wins over inverted entropy of fuel.
And here's a related question and answer from an FAQ of the subreddit:
How did the reverse bullet holes get into the wall in the first place?
How long has the glass in the Oslo Turnstile been broken?
What happened to the flipped car on the highway? Shouldn't that have been there before the car chase? Who put it there?
The Movie doesn't want you to worry about such details it too much.
This is a nasty little logic problem that throws the premise of a lot of the Movie's spectacular set-pieces somewhat into question.
The Movie does attempt an explanation. When in the container on their way to Oslo Neil explains that our universe has a prevailing direction of entropy - a "wind". Events that go against the wind will eventually succumb to it.
Here is how that could work in practice: At first the glass at the Oslo Turnstile is normal and unbroken. A few hours before the events the glass becomes somewhat brittle in some spots. A micro fracture develops which slowly grows to become more and more pronounced over time. Small pieces start falling off. Eventually the fracture starts looks like a bullet hole. This is when our Protagonist enters the room.